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127/1000, this is actually easy! fundamental theorem of calculus

• bprp calculus b… 20일 전 2026.09.11 16:00 인기
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@Mediterranean8… 　19일 전

∫ sec x dx = arctanh(sin x) + C

2026-09-12 07:11

[ytcid:UgyS-JxKuv1GCvFs-Tp4AaABAg] ∫ sec x dx = arctanh(sin x) + C



@davidgillies62… 　19일 전

The integral itself is arctanh(t). So you can sub in sin(x) and 2 for the bounds and differentiate and you get the same result of sec(x) after simplifying (which is nice).

2026-09-12 07:02

[ytcid:UgwqkSAcWic3ek5tTgd4AaABAg] The integral itself is arctanh(t). So you can sub in sin(x) and 2 for the bounds and differentiate and you get the same result of sec(x) after simplifying (which is nice).



@יאירמרוז 　19일 전

The 2 is ignored because ita derivatives into 0 because when u plague in 2 it's a constant

2026-09-12 05:56

[ytcid:Ugx52V3kzhXeg7aQ85N4AaABAg] The 2 is ignored because ita derivatives into 0 because when u plague in 2 it's a constant



@paultoutounji3… 　19일 전

Why is the 2 ignored ?

2026-09-12 05:40

[ytcid:Ugz2y9lHNoRif7nJX1B4AaABAg] Why is the 2 ignored ?



@SEWER616 　19일 전

Is it sin^2(x) or (sin(x))^2

2026-09-12 05:07

[ytcid:UgyxxT1CBg7UFbFOtFZ4AaABAg] Is it sin^2(x) or (sin(x))^2



@major__kong 　19일 전

I've been an engineer for about 30 years. I've never seen this used in practice. Maybe it has special significance in the math world?

2026-09-12 04:42

[ytcid:Ugwp7nAHnoc-ttNNeul4AaABAg] I've been an engineer for about 30 years. I've never seen this used in practice. Maybe it has special significance in the math world?



@BrianOxleyTexa… 　20일 전

I do not understand how the lower bound of 2 in the integral comes into play. What if that were -1 or pi or something else?

2026-09-12 03:09

[ytcid:UgyqvohNedMMFEurCxR4AaABAg] I do not understand how the lower bound of 2 in the integral comes into play. What if that were -1 or pi or something else?



@brainfellow514… 　20일 전

What happened to the lower bound 2?

2026-09-11 22:54

[ytcid:UgzhgAyXKX0ifqJIkHt4AaABAg] What happened to the lower bound 2?



@MisterJackTheA… 　20일 전

Well i did get it wrong on the exams, hence I'm a cashier with above average math skills.

2026-09-11 22:23

[ytcid:Ugw_iCD8fYdjR7ddFJt4AaABAg] Well i did get it wrong on the exams, hence I'm a cashier with above average math skills.



@ImadAjjaj 　20일 전

127 out of 1000

2026-09-11 18:29

[ytcid:UgyZLONF6px5gfLegV54AaABAg] 127 out of 1000



@vikramrawat526… 　20일 전

Day 127

2026-09-11 17:10

[ytcid:UgxvofHk5Qw9DZ1Rrld4AaABAg] Day 127



@K2MusicKSquare 　20일 전

Never see this before. Why is the 2 ignored?

2026-09-11 16:48

[ytcid:UgxwhWnTHYyvXn277r94AaABAg] Never see this before. Why is the 2 ignored?



@sciphyskyguy43… 　19일 전

What are examples of questions that you _do_ want to get wrong?;-)

2026-09-13 02:07

[ytcid:UgxMAe-BmTwhbydImfB4AaABAg] What are examples of questions that you _do_ want to get wrong?;-)



@Keithfert490 　19일 전

This is actually undefined because the integrand is not defined in the entire interval [sin(x),2]

2026-09-13 01:53

[ytcid:UgxzbzMicqDD0gNhKaN4AaABAg] This is actually undefined because the integrand is not defined in the entire interval [sin(x),2]



@liruizhu2146 　19일 전

Isn't this the leibniz integration rule?

2026-09-12 10:12

[ytcid:Ugz4d-esP0dWF-dDbWJ4AaABAg] Isn't this the leibniz integration rule?



@elSplunky 　17일 전

When you evaluate the integral you get tanh^-1(sinx) - tanh^-1(2). Then differentiate w.r.t. x, you get cosx / (1 - sin²x), which simplifies to secx.

2026-09-14 22:10

[ytcid:Ugw7dvdEH_2anfCIXVJ4AaABAg] When you evaluate the integral you get tanh^-1(sinx) - tanh^-1(2). Then differentiate w.r.t. x, you get cosx / (1 - sin²x), which simplifies to secx.